Question

The points $(2,1),(5,4)$ and $(1,4)$ are three of the corners of a parallelogram. Find the coordinates of the remaining corner which is opposite to $(2,1)$

Answer 1

$\frac{A+C}{2}=\frac{B+D}{2}$

$\frac{a+2}{2}=\frac{5+1}{2}\Rightarrow a+2=6$

$a=4$

$\frac{b+1}{2}=\frac{4+4}{2}\Rightarrow b+1=8$

$b=7$

$(4,7)$